First, make the pie dough. Thinly slice ½ cup (one stick) of butter. Add shavings to a bowl and freeze for 30 minutes.
To a food processor, add flour, salt and sugar and pulse to mix. Add the butter and pulse until the butter is broken up and well distributed throughout the flour. Add 4-5 tablespoons of ice water and pulse until the dough just comes together.
Tip the course pie dough out onto a hard surface that has been lined with plastic wrap. Using the sides of the plastic wrap, pull the dough together and into a disc. Wrap the pie dough completely in plastic wrap and refrigerate the pie dough for 2 hours or overnight.
When ready, make the cherry pie filling. Wash, pit and halve 3 heaping cups of fresh sweet cherries. Add to a bowl, along with the sugar, almond extract, cornstarch and salt. Stir to mix. Set aside.
Place the cold pie dough onto a large piece of parchment paper that has been dusted in flour. Roll the dough out into a 12-inch diameter circle. Slide the pie dough (and parchment paper) onto a short-rimmed baking sheet. Dust the interior of the pie dough circle with semolina flour, leaving a 2-inch border around the pie round. Dump the cherry filling into the middle of the pie round and fold the border in on itself, crimping the edges as you work around the pie dough.
Brush the edges of the galette with an egg wash (one egg whisked together with 1 tablespoon of cold water), then sprinkle the entire pie and edges with coarse sugar.
Bake the galette at 400°F for 32-35 minutes or until golden brown and bubbly.
Let cool on a wire rack completely before slicing and serving.
This recipe makes one 9-inch galette, or 8 small slices.